Groups acting on fractals – GOFR

Groups appear in all domains of mathematics and have ramifications in other scientific domains, as physics, computer science, biology, and even art and design. To a finitely generated group, one can associate a graph, that makes this group a metric space, with a set of symmetries. Group theory allows to, at the same time, construct and study graphs of arbitrarily high complexity, as expanders for instance, that have important applications in network theory, computer science, cryptography, and modelisation. The properties that we intend to study in this project are large scale properties of infinite discrete groups: dimensions, growth functions, large-scale curvature. Often, a limiting object, obtained by a rescaling process, encapsulates some of these properties: for instance, boundaries, or limit R-tree of a sequence of actions, or limit fractal of self-similar actions. The aim is to extract algebraic and structural insight from geometry and fractalness of these objects.